7ed5/4: Difference between revisions

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'''7ED5/4''' is the [[Equal-step tuning|equal division]] of the [[5/4|just major third]] into seven parts of 55.1877 [[cent|cents]] each, corresponding to every fourth step of [[87edo]]. It is related to the 5-limit temperament which tempers out |234 -7 -96> (0.198463 cents, 5-limit 1783&7980 comma).

'''7ED5/4''' is the [[Equal-step tuning|equal division]] of the [[5/4|just major third]] into seven parts of 55.1877 [[cent|cents]] each, corresponding to every fourth step of [[87edo]]. It is related to the [[Hemifamity temperaments|alphaquarter temperament]] and the 5-limit temperament which tempers out |234 -7 -96> (0.198463 cents, 5-limit 1783&7980 comma).

==Intervals==

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| | (5/4)<font style="vertical-align:super;font-size:0.8em;">13</font> = 1220703125/67108864

|}

==7ED5/4 as a generator==

===Alphaquarter===

7ED5/4 leads the alphaquarter temperament using its three steps for [[11/10]], its nine steps for [[4/3]], and its 61 steps for [[7/1]]. Alphaquarter tempers out 3025/3024, 4000/3993, and 5120/5103 in the 11-limit, supported by [[87edo]], [[152edo]], [[239edo]], and [[391edo]].

===1783&7980 temperament===

7ED5/4 leads 1783&7980 temperament using its 96 steps for 64/3 (four octaves plus just perefect fourth).

Comma: |234 -7 -96>

POTE generator: 55.188

Map: [<1 6 2|, <0 -96 7|]

EDOs: [[1783edo|1783]], 4414, 6197, [[7980edo|7980]], 9763, 11546, 14177

Badness: 0.1157

[[Category:5/4]]

[[Category:Equal-step tuning]]

[[Category:Edonoi]]

@@ Line 1: / Line 1: @@
-'''7ED5/4''' is the [[Equal-step tuning|equal division]] of the [[5/4|just major third]] into seven parts of 55.1877 [[cent|cents]] each, corresponding to every fourth step of [[87edo]]. It is related to the 5-limit temperament which tempers out |234 -7 -96&gt; (0.198463 cents, 5-limit 1783&amp;7980 comma).
+'''7ED5/4''' is the [[Equal-step tuning|equal division]] of the [[5/4|just major third]] into seven parts of 55.1877 [[cent|cents]] each, corresponding to every fourth step of [[87edo]]. It is related to the [[Hemifamity temperaments|alphaquarter temperament]] and the 5-limit temperament which tempers out |234 -7 -96&gt; (0.198463 cents, 5-limit 1783&amp;7980 comma).
 ==Intervals==
@@ Line 376: / Line 376: @@
 | | (5/4)<font style="vertical-align:super;font-size:0.8em;">13</font> = 1220703125/67108864
 |}
+==7ED5/4 as a generator==
+===Alphaquarter===
+ED5/4 leads the alphaquarter temperament using its three steps for [[11/10]], its nine steps for [[4/3]], and its 61 steps for [[7/1]]. Alphaquarter tempers out 3025/3024, 4000/3993, and 5120/5103 in the 11-limit, supported by [[87edo]], [[152edo]], [[239edo]], and [[391edo]].
+===1783&amp;7980 temperament===
+ED5/4 leads 1783&amp;7980 temperament using its 96 steps for 64/3 (four octaves plus just perefect fourth).
+Comma: |234 -7 -96&gt;
+POTE generator: 55.188
+Map: [&lt;1 6 2|, &lt;0 -96 7|]
+EDOs: [[1783edo|1783]], 4414, 6197, [[7980edo|7980]], 9763, 11546, 14177
+Badness: 0.1157
 [[Category:5/4]]
 [[Category:Equal-step tuning]]
 [[Category:Edonoi]]